Polynomial operations involve basic mathematical processes applied to polynomials, which are expressions made up of variables and coefficients. The main operations include addition, subtraction, multiplication, and division. When adding or subtracting polynomials, like terms (terms with the same variable and exponent) are combined. In multiplication, polynomials are expanded using the distributive property, often resulting in a polynomial of higher degree. Division of polynomials can be more complex, typically involving long division or synthetic division. Understanding these operations is essential for solving equations and analyzing functions in algebra and calculus, particularly in topics related to functions and graphing.